I have a matrix in $\mathbb{R}^{m \times n}$ where each entry $a_{ij}$ depends from a different vector variable, namely
$$ a_{ij} = a_{ij}(x_1^i,x_2^j) $$
So in case $m = n = 2$ it would be something like
$$ A(\vec{x})=\begin{pmatrix} a_{11}(x_1^1,x_2^1) & a_{12}(x_1^1,x_2^2) \\ a_{21}(x_1^2,x_2^1) & a_{22}(x_1^2,x_2^2) \end{pmatrix}, $$
And I do wonder if there's a notation that can be used to express the gradient of $A$, and generalize for generic $m,n$.
The only clue I have would be using tensors, but I'm not particularly familiar with them so If someone can help me out with this I would really appreciate it.